21st Century COE Program : Mathematics of Nonlinear Structure via Singularity

UMEDA, Noriaki : COE Lecture Series

On Global Existence and Blow-up of Solution of some Reaction-Diffusion Equations

My study has focused on non-negative solutions to the initial value problem surrounding reaction-diffusion equations and systems. Solutions to such equations formally represent various reaction-diffusion phenomena, including temperature changes in substances that are caused by chemical reactions, as well as changes in the numbers of individuals that exist in a mathematical ecology. Ever since Hiroshi Fujita's seminal work in 1966, much research has been done in this area. In particular, a number of researchers are still actively studying the blow-up of solutions in finite time and the existence of global solutions to reaction-diffusion equations. In this talk, I am going to discuss a few aspects of this vast area of research, with special attention to evaluation methods for blow-up and global solutions to such equations.
21st Century COE Program : Mathematics of Nonlinear Structure via Singularity